That ignores the fact that Bismarck also had serious damage, and turning back would have brought Norfolk and Suffolk into action. Prinz Eugen couldn't take them both on, and their toropedoes were a serious threat.
The same is on the German side, Helmuth Brinkman wanted to launch a torpedo attack on HMS Prince of Wales in OTL, but Günther Lütjens ordered a retreat. In TTL, if HMS Hood is still in the fight, Prinz Eugen goes after her and tries to torpedo her, whether she succeeds is another question. But I repeat, Helmuth Brinkman would have carried out the torpedo attack.
Assuming she was able to fight her way past PoW and the cruisers, and assuming that if she was able to do that she didn't run into the rest of the Home Fleet (KGV, Repulse, Victorious, etc), and even if she'd been able to do that she would still be left with the problem of repeating her attempted breakout. Lutjens knew what he was doing when he decided to make for Brest instead of reversing course.
Günther Lütjens did not withdraw from the battle because Bismarck was damaged, he withdrew from the battle because such were his operational orders. And the British allowed him to withdraw because they were trying to escape in OTL. And Captain John Leach knew very well why he was running, because to continue the battle was suicide.
Lütjens did not go to France immediately after the battle, that is a myth. He wanted to sail to Belchen to refuel. His original plan was that he wanted to continue the mission. But it turned out that it was not possible. It wasn't until a few hours after the battle, when he received news from his technicians, that he headed for Brest. So he had to cancel his original plan because he was running out of fuel and he paid the price for somehow forgetting to fill it up already in Bergen. When he had a great opportunity to do so.
The home fleet was too far away, they couldn't stop him in OTL, they wouldn't even be able to stop him in TTL. Lütjens had a huge opportunity on May 24, 1941, which he squandered through his stupidity. Throughout the mission, he followed orders that expired as early as five o'clock in the morning on May 24.
Otherwise to the shooting of HMS Hood, it shot poorly..., Prinz Eugen hit it within the first minute of the fight. Bismarck hesitated to fire and her guns fell silent for several minutes before Lindemann took charge. And ordered to open fire on HMS Hood. Those few minutes may have been decisive. HMS Hood could well have exploded two or three minutes earlier than in OTL. If at the beginning of the battle Günther Lütjens had not hesitated whether to fight or not. All along he tried to avoid action, he gave the British a chance, they didn't take it. And then he did everything to prepare himself for a crushing victory.